For each linear transformation below, state a basis for Ker(T), the Nullity of the transformation, and the Rank of the transformation. If you do notneed a vector, then place zeros for all entries of that vector (for example, if you only need 2 vectors for the basis, then fill in the firsttwo vectors and make all subsequent vectors have 0 for all boxes).a1) Let T b- B - Lla+1b+1c2a+3b+3c]-la + (-2)b+ (-2)c 3a+3b+3ci) A basis for Ker(T) would be:ii) The Nullity of T is:iii) The Rank of T is:2) Let T(a + bx + cx² + dx³) =i) A basis for Ker(T) would be:ii) The Nullity of T is:iii) The Rank of T is:3) Let Tab[ d f[def=1a2b+1c + 1d[la+16+2c+2d2a+36 + 4c+ 2d -la + (-3)6 + (-1)c+2d]la+(-1)b+1c+ (-1)d + 2e+4f2a+(-1)b+4c+4d + 6e + 12fOa+(-1)b+(-1)c+ (-4)d + (-1)e + (-2) f6a+(-3)b+11c + 10d + 18e + 34fi) A basis for Ker(T) would be:

For a linear transformation T, the kernel (Ker(T)) is the set of all vectors that are mapped to the…

Answered: For each linear transformation below,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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For each transformation below, determine a basis for (Ker(T))↓. Note that if you do not need a basis vector, then write 0 for all entries of that basis vector. For example, if you only need 2 vectors in your basis, then write 0 in all boxes corresponding to the third vector 1) Let T c = 1a + 2b + 1c+3d + (−11) e+ (−la + (−1) b + (−2) c + Od + 7e) x. El Then a basis for (Ker(T)) would be:
Question 6 of 16 Ali, the CEO of a manufacturing company, decided to expand the product offering of his business to include the manufacture of a specific model automotive unit. To include this product, his business would incur fixed costs of $365,000 per year and variable costs of $6 per unit. He plans to sell each unit for $88. a. Calculate the number of units he would have to manufacture to break even. Round up to the next whole number b. While manufacturing the unit, he realized that an additional fixed cost of $3,000 per year was required, and also realized that to be more competitive in the market he had to drop the selling price by 20%. What is the new break-even volume? Round up to the next whole number

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